I absolutely agree with you on almost everything here. Much of it is what led me to my hypothesis for the cause.
Why would religion seem to have such a strong relationship with healthier birth rates? The obvious responses don't really work out. The Bible is surprisingly ambiguous on how many children people should have, or even if everybody should endeavor to do so. And in any case, people scarcely follow the teachings of the Bible when even moderately inconvenient.
Looking to past, in ancient times philosophy meant something different than today. Essentially everybody was expected, as a part of becoming an adult, to develop their own philosophy of life. Ancient religions offered very little in the way of life philosophy. Pre-Abrahamic religions, such as in Greek or Norse culture, had Gods which took on all human characteristics - maliciousness, greed, sadism, and more. The stories offered were metaphorical in nature, rather than something to guide your life by. So this is the era where you get people inventing everything from the Cult of Pythagoras to Zenoism (stoicism).
But in modern times we, in general, no longer have religion and we no longer have philosophy. So what have people turned to guide them in life? And the answer seems largely to be Product. Eternal happiness is always just one new Product away. And not only have many people turned to Product, but there has been an increasing trend of people denying their own mortality - whether through some sort of singularity event, the 'marvels of medicine' somehow growing exponentially to enable people to live indefinitely, or even some fringe quantum immortality views.
What alternative philosophies are emerging seem to also be death cults in any case - viewing humans as little more than machines, rejecting ones own consciousness, and so on. In all of these philosophies and world views there seems to be very little reason for children. And it just so happens that when one starts to look at things from this perspective, it somehow explains everything literally perfectly. I've yet to find a single compelling exception, while every other explanation for fertility just completely falls to pieces under the slightest of scrutiny.
